Conservative Republicans in Kansas are looking to drive the party's centrists from the state legislature in primaries next month in a bid to turn the state an even deeper shade of red.

Long a conservative state, Kansas already has been shifting further right, particularly since 2010, when Sam Brownback was elected governor and Republicans backed by the tea-party movement won control of the state House of Representatives. Now, challengers backed by conservative groups including the Kansas Chamber of Commerce and Americans for Prosperity are aiming to unseat a dozen centrist Republicans in the 40-member Senate, the last part of the statehouse that, combined with a handful of Democrats, can mount opposition to Mr. Brownback and the House.

The Kansas intra-party conflict echoes many of the same themes playing out in other states. But there’s an even longer history of tension there and over the past two decades it’s proved costly to the GOP in this conservative state. Among the consequences: the 2002 election of former Democratic Gov. Kathleen Sebelius, who currently plays on a much larger stage as HHS Secretary.